First a simple question, another name of UR starts with a “K”, what is it? I’m drawing a blank! lol
Second, what do you think is the best name for Universal Reconciliation, or what do you think the various ways it is referenced connotes?
I can’t think of anything that starts with “k” but might you be thinking of apokatastasis? It has a “k” in it anyway. 
Personally, I like Universal Reconciliation better than Universalism. The term “universalism” carries a lot of associations with it–people think they know what it means already, and it sets off the automatic “heresy” alarms. 
Sonia
I too like Universal Reconciliation much better than Universalism or even Christian Universalism because of all the bagage of assumptions and misconceptions attached to Universalism.
I suppose I’m specifically looking for a good one-word-ism, that flows with Augustinianism, Calvinism, and Arminianism.
I’m a fan of “UR” more than “EU.” I also like apocatastasis, but that has negative connotations in some people’s minds to some of the weirder thoughts of Origen (like pre-existence of souls, people cycling between heaven and hell, and so forth). I think “evangelical universal reconciliation” describes it, but that’s a bit long. 
Jason P uses the term “Kath,” but I forgot where he explained the origin of that. Oftentimes he abbreviates the three main theological positions Calv, Arm, and Kath, which is obviously Calvinism, Arminianism, and… ? Little help here? 
“Katholic”, that’s the word I was looking for. I think though that this would be confusing, especially if “heard”, not read. I wonder if “Reconciliationist” (Rec) would work? Hmm.
I like Evangelical Universalist even though I’m not keen on “Evangelical” by itself because that has negative connotations. But smoosh it together with “Universalist” and bada-bing! You have an interesting paradox that makes people stop and think.
Reconciliationist is probably a real good short name that would make people stop and wonder what you mean by it. I like that.
Stellar, I like your term “reconciliationist” and have already used it. However, if it it isn’t prefixed by “universal” then it can be taken to mean simply one who believes in reconciliation to God, and that would encompass virtually all Christians.
I strongly oppose the term “universalist” and never call myself by that appelation, for in virtually everyone’s mind it means someone who believes everyone will go to heaven automatically.
A rather descriptive term would be “dominionist”, but unfortunately that term has already been applied to those who would make Christianity a political entity, not to mention various other applications of the word.